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Which of the following is equivalent to 6x 2 + x - 12 ?
A. (2x + 3)(3x - 4)
B. (2x - 3)(3x - 4)
C. (2x + 3)(3x + 4)
D. (6x + 3)(x - 12)
E. (x + 3)(2x - 12)
Please show me step by step how to solve this problem
Thanks

Sagot :

[tex]6x^2+x-12=6x^2-9x+8x-12=3x(2x-3)+4(2x-3)\\\\=(2x-3)(3x+4)\\\\other\ method:\\\\6x^2+x-12\\a=6;\ b=1;\ c=-12\\\Delta=b^2-4ac\to\Delta=1^2-4\cdot6\cdot(-12)=1+288=289\\\\x_1=\frac{-b-\sqrt\Delta}{2a};\ x_2=\frac{-b+\sqrt\Delta}{2a}\\\\\sqrt\Delta=\sqrt{289}=17[/tex]

[tex]x_1=\frac{-1-17}{2\cdot6}=\frac{-18}{12}=-\frac{3}{2};\ x_2=\frac{-1+17}{2\cdot6}=\frac{16}{12}=\frac{4}{3}\\\\6x^2+x-12=6(x+\frac{3}{2})(x-\frac{4}{3})=2\cdot3(x+\frac{3}{2})(x-\frac{4}{3})\\\\=2(x+\frac{3}{2})\cdot3(x-\frac{4}{3})=(2x+3)(3x-4)[/tex]
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